Table 1.
The nonlinear equation system’s norms are shown, and the COC is bolded and enclosed in parenthesis.
Fig 1.
Dynamics of proposed method when a line and circle intersect, the number of iterations are ten and tolerance is 0.01.
Fig 2.
Dynamics of proposed method when a circle and circle intersect, the number of iterations are ten and tolerance is 0.01.
Fig 3.
Dynamics of proposed method when a parabola and circle intersect, the number of iterations are ten and tolerance is 0.01.
Fig 4.
Dynamics of proposed method when a hyperbola and circle intersect, the number of iterations are ten and tolerance is 0.01.
Fig 5.
Numerical solution of Blasius equation.
Fig 6.
Derivative of numerical solution of Blasius equation.
Table 2.
COC of proposed method (2) for the numerical solution of Blasius equation.
Fig 7.
Numerical solution of Falkner-Skan equation for β =4 /3.
Fig 8.
Derivative of numerical solution of Falkner-Skan equation for β =4 /3.
Table 3.
COC of proposed method (2) for the numerical approximation of Falkner-Skan equation (β =4 /3).
Fig 9.
Numerical solution of Lane-Emden equation for n = 2.
Fig 10.
Derivative of numerical solution of Lane-Emden equation for n = 2.
Fig 11.
Numerical solution of nano-particles in fluid.
Fig 12.
Derivative of numerical solution of nano-particles in fluid.
Fig 13.
Numerical solution of natural convection (Pr = 1).
Fig 14.
Derivative of numerical solution of natural convection (Pr = 1).
Fig 15.
Numerically computing solution of 2-D partial differential equation.
Fig 16.
Absolute error in the computed solution of 2-D partial differential equation.
Table 4.
Average simulation elapsed times for the comparison of Newton and our proposed method.